Read the following definition carefully, and then answer the questions below. i We define an n x n matrix A to be passive if A? = A. Note: before diving in to solving the questions below, you may wish to try to create some examples of passive mat rices (say 2 × 2 to keep it simple). 21 Suppose that A is passive. Show that I – A is also passive but A – I is not passive. 22 True or False:' if A is m x n and B is n x m and AB = Im, then BA is passive. 23 Show that if A is a passive 2 x 2 matrix with non-zero entries, then the sum of the entries on the diagonal of A is equal to 1. Create an example of such a matrix and show that it is indeed passive. (That is, if A : [a b is passive and has a, b,c,d + 0, then a +d = 1.) 2.
Read the following definition carefully, and then answer the questions below. i We define an n x n matrix A to be passive if A? = A. Note: before diving in to solving the questions below, you may wish to try to create some examples of passive mat rices (say 2 × 2 to keep it simple). 21 Suppose that A is passive. Show that I – A is also passive but A – I is not passive. 22 True or False:' if A is m x n and B is n x m and AB = Im, then BA is passive. 23 Show that if A is a passive 2 x 2 matrix with non-zero entries, then the sum of the entries on the diagonal of A is equal to 1. Create an example of such a matrix and show that it is indeed passive. (That is, if A : [a b is passive and has a, b,c,d + 0, then a +d = 1.) 2.
Transcribed Image Text:Read the following definition carefully, and then answer the questions below.
i We define an n x n matrix A to be passive if A? = A.
Note: before diving in to solving the questions below, you may wish to try to create some
examples of passive mat rices (say 2 × 2 to keep it simple).
21 Suppose that A is passive. Show that I – A is also passive but A – I is not passive.
22 True or False:' if A is m × n and B is n x m and AB = Im, then BA is passive.
23 Show that if A is a passive 2 x 2 matrix with non-zero entries, then the sum of the
entries on the diagonal of A is equal to 1. Create an example of such a matrix and
show that it is indeed passive.
(That is, if A :
Ja b
is passive and has a, b, c, d # 0, then a+d = 1.)
2.
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